By Keigo Iizuka; John Wiley & Sons, Inc
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Extra resources for Elements of Photonics, Volume II : For Fiber and Integrated Optics
The field distributions for the first few mode orders. The correlation of the region of ˇ with the field pattern and directions of propagation of the component plane waves. Solution The change in the index of refraction at the air–film interface is much greater than that at the film–substrate interface. 14 Geometry of an asymmetric slab optical guide. 640 PLANAR OPTICAL GUIDES FOR INTEGRATED OPTICS internal reflection for the film–substrate is satisfied, that for the air–film is automatically satisfied.
If d2 ! 0, then A D 0 and Eq. 131) immediately reduces to Eq. 72). If n2 ! n0 and hence 2 ! 0 , then B in Eq. 132) approaches unity because Eq. 72) can be approximately used in Eq. 132), and Eq. 131) approaches Eq. 72). The procedure for calculating ˇ for given physical parameters will be described. From Eqs. 135 From Eqs. 137 Similarly, from Eqs. 139 The procedures to find ˇ are as follows: 1. Calculate both V0 and V2 from Eqs. 139). 2. Use 2 d1 D V22 K1 d1 2 to calculate 2 d1 for a given K1 d1 .
107) has to be zero. 108 where the values of Z0 and ZN are available from Eqs. 105) and the matrix elements A, B, C, and D are obtained after calculating the product of the T’s in Eq. 99). 6. 3 Transmission Matrix Method (Symmetric Guide) If symmetry exists in the distribution of the indices of refraction, the computation becomes significantly simpler. Let us say, as shown in Fig. 10, symmetry exists with respect to x D 0 and the indices of refraction from the bottom to the top layer are arranged as n0 , n1 , n2 , .
Elements of Photonics, Volume II : For Fiber and Integrated Optics by Keigo Iizuka; John Wiley & Sons, Inc